Field of the Invention
The present invention relates to optical systems for real-time matrix-matrix multiplication. In particular, the present invention relates to wavelength multiplexed matrix-matrix multiplication systems using spatially coherent light sources.
Discussion of Related Art
In the 1970s P. N. Tamura and J. C. Wyant described optical systems for multiplying a matrix by a matrix in a series of steps (only vector-matrix multiplication in real-time is accomplished. To perform matrix-matrix multiplication, a mechanical system is necessary). FIGS. 1(a) and 1(b) (prior art) show an example from “Two-Dimensional Matrix Multiplication using Coherent Optical Techniques,” Optical Engineering, Vol. 18, No. 2, March-April 1979, pp. 198-204. FIG. 1(a) is a side isometric schematic drawing showing the optical elements of the system. FIG. 1(b) is a flow diagram showing the functions performed. A plane wave is focused to a line by a cylindrical lens L1. The matrix B element is movable vertically to allow one row of matrix B (i.e. a vector) to be illuminated and pass through the system at a time. Matrix B and matrix A were implemented as transparencies. A horizontally sliding slit at the system exit selects the appropriate result column for that vector. lenses L1, L3 and L6 are used to perform the fundamental mathematical operations, and the lenses L2, L4, L5 and L6 used in 4F-setups to avoid diffraction issues. Group L2L3L4 takes an image in x and Fourier transform in y. Group L5L6L7 takes an image in y and Fourier transform in x.
A need remains in the art for apparatus and methods to accomplish matrix-matrix multiplication in a single set of operations.